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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Unicellular operators


Authors: José Barría and Kenneth R. Davidson
Journal: Trans. Amer. Math. Soc. 284 (1984), 229-246
MSC: Primary 47A15; Secondary 47A45, 47B37
DOI: https://doi.org/10.1090/S0002-9947-1984-0742423-2
MathSciNet review: 742423
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Abstract: An operator is unicellular if its lattice of invariant subspaces is totally ordered by inclusion. The list of nests which are known to be the set of invariant subspaces of a unicellular operator is surprisingly short. We construct unicellular operators on ${l^p},1 \leqslant p < \infty$, and on ${c_0}$ with lattices isomorphic to $\alpha + X + {\beta ^{\ast }}$ where $\alpha$ and $\beta$ are countable (finite or zero) ordinals, and $X$ is in this short list. Certain other nests are attained as well.


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Keywords: Unicellular operator, invariant subspaces, attainable lattices
Article copyright: © Copyright 1984 American Mathematical Society